Tension in Rope: Force, Acceleration & Intuition

In summary: This is not true.@PhanthomJay But f=ma, and since there is no acceleration, how can there be tension? If there is, what is the answer to the question?I think it is 0.
  • #1
sumitsumit
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Homework Statement
What will be the tension on the rope? Suppose a rope at attached to the wall and a car and the car starts to move a velocity v in right direction.
Relevant Equations
tension, velocity,
i believe there must be some tension while for the force to exert there must be acceleration but my intuition says different
 

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  • #2
Why do you expect no tension in the rope? There can exist tension in the rope without accceleration . Please clarify your thoughts on this.
 
  • #3
@PhanthomJay But f=ma, and since there is no acceleration, how can there be tension? If there is, what is the answer to the question?

I think it is 0.
 
  • #4
Pi-is-3 said:
@PhanthomJay But f=ma, and since there is no acceleration, how can there be tension? If there is, what is the [answer to the question?

I think it is 0.
well , we don’t give answers, but here’s A hint: in the equation f= ma, f is the net force acting on the rope. So if a is 0, net force is zero, and if the car is pulling with a force on the rope, there must be another force acting on the rope to give a net force of 0. What is it? Surely you’ve seen a vehicle trying to pull another out of the mud, and neither vehicle is moving in spite of the first one with pedal to the floor, and the rope is pretty tight , right?
 
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  • #5
sumitsumit said:
Problem Statement: What will be the tension on the rope? Suppose a rope at attached to the wall and a car and the car starts to move a velocity v in right direction.
This description is most unclear.
Pi-is-3 said:
since there is no acceleration
Does the car suddenly go from stationary to speed v? How does it "start to move" with no acceleration?
Is the rope already taut or does it start slack?
 
  • #6
haruspex said:
This description is most unclear.

Does the car suddenly go from stationary to speed v? How does it "start to move" with no acceleration?
Is the rope already taut or does it start slack?
I have no idea how it starts. I didn't start the thread @sumitsumit did. Honestly I am more confused by what @PhanthomJay said.
 
  • #7
Pi-is-3 said:
I have no idea how it starts. I didn't start the thread @sumitsumit did. Honestly I am more confused by what @PhanthomJay said.
The correct equation is Σf=ma, i.e. the acceleration results from the sum of all forces. The tension in the rope is only one force on the car; there may be others.
 
  • #8
Pi-is-3 said:
I have no idea how it starts. I didn't start the thread @sumitsumit did. Honestly I am more confused by what @PhanthomJay said.
Well perhaps here is a better example...a game of ‘tug of war’. Your team is pulling on one end of the rope, trying to move the opposing team. And the opposing team is pulling the rope on the other end, trying to move your team. But assume strengths and foot holds of each team are the same, so no one is going anywhere. It’s a stalemate. There is no acceleration. Now you are trying to tell me there is no tension in the rope? There is a lot of tension , the rope might be close to breaking if it’s not strong enough. Think about Newton’s first law and draw a free body diagram of the rope from one end to an imaginary cut in-the center.
 
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  • #9
PhanthomJay said:
Well perhaps here is a better example...a game of ‘tug of war’. Your team is pulling on one end of the rope, trying to move the opposing team. And the opposing team is pulling the rope on the other end, trying to move your team. But assume strengths and foot holds of each team are the same, so no one is going anywhere. It’s a stalemate. There is no acceleration. Now you are trying to tell me there is no tension in the rope? There is a lot of tension , the rope might be close to breaking if it’s not strong enough. Think about Newton’s first law and draw a free body diagram of the rope from one end to an imaginary cut in-the center.
Now I get it. Thanks!
 
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  • #10
And also, if you think of the rope as consisting of a large number of really short segments that are connected to the segment before and after them, then each such segment experiences the same but opposite force from both directions if there is no acceleration.

Then there is the concept of stress, which is tension divided by cross-sectional area and therefore has units of pressure and can vary along the rope if it's not equally thick everywhere.
 
  • #11
Pi-is-3 said:
@PhanthomJay But f=ma, and since there is no acceleration, how can there be tension? If there is, what is the answer to the question?

I think it is 0.
Please tell me that you believe that you can’t have a force without acceleration.
 

What is tension in a rope?

Tension in a rope is the force that is exerted by the rope when it is pulled taut. It is the result of the forces acting on the rope, such as the weight of an object hanging from the rope or the force applied to the rope by a person pulling on it.

How is tension related to force?

Tension and force are directly proportional to each other. This means that as the force applied to the rope increases, the tension in the rope also increases. Similarly, if the force decreases, the tension in the rope will also decrease.

What is the relationship between tension and acceleration?

The relationship between tension and acceleration is described by Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it. In the case of a rope, the tension in the rope is one of the forces acting on the object, and the acceleration of the object is dependent on the tension in the rope.

How does intuition play a role in understanding tension in a rope?

Intuition plays a crucial role in understanding tension in a rope. Our intuition tells us that when we pull on a rope, it becomes taut and the tension increases. Similarly, when we release the rope, the tension decreases. Our intuition also helps us understand the relationship between tension, force, and acceleration, as we can intuitively understand that a greater force applied to the rope will result in a greater tension and therefore a greater acceleration of the object attached to the rope.

What factors can affect tension in a rope?

There are several factors that can affect tension in a rope, including the weight of the object attached to the rope, the force applied to the rope, and the properties of the rope itself, such as its elasticity and strength. The angle at which the rope is pulled can also affect tension, as well as any friction or obstacles in the path of the rope. Additionally, external factors such as wind or other forces acting on the object can also impact the tension in the rope.

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